Gauss' Law conductors

1. The problem statement, all variables and given/known data
Three concentric hollow spherical conductors are charged as follows: the inner conductor carries charge Q, the middle conductor carries charge -2Q, and the outer conductor carries charge -Q. What is the charge on the outer surface of the middle conductor?

2. Relevant equations
Flux= Qenc / ε0

3. The attempt at a solution

Because the flux inside a conductor has to be zero, I drew a gaussian surface in the second conductor, since the first conductor is carrying Q, the inner surface of the 2nd conductor should carry -Q, and the outer surface, to neutralize that should carry Q.

Doen't the inside of the conductor itself have to have no electric field? and if you have uneven charges there would be a field? And if the total charge of the second conductor is -2Q, and the inner surface is -Q, then they just are additive and the outer surface becomes -Q?